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LUSTERNIK-SCHNIRELMANN THEORY TO TOPOLOGICAL COMPLEXITY FROM A∞-VIEW POINT

IWASE, Norio 岩瀬, 則夫 イワセ, ノリオ 九州大学

2023.02.26

概要

In this article, we work in the category of CW-complexes and maps between
them, but we often restrict ourselves into the full subcategory of pointed CWcomplexes. The pointed and unpointed theories are very close in the usual
homotopy theory, but we find that they are far apart, if we discuss the higher
associativity of an H-space fibrewise, or parametrized. Before starting the main
part, we discuss about the higher associativity of an H-space, which is closely
related to both (fibrewise) L-S theory and TC.
2020 Mathematics Subject Classification. Primary 55M30; Secondary 18M75, 55P05,
55P10, 55P45, 55P48, 55Q25, 55R35, 55R70, 55S10.
Key words and phrases. Lusternik-Schnirelmann category, topological complexity, fibrewise theory, A∞ -structure, classifying space.
The author was supported in part by Grant-in-Aid for Scientific Research (S) #17H06128
and by Exploratory Research #18K18713 from Japan Society for the Promotion of Science. ...

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Manuscript received MONTH 00, 0000

accepted MONTH 00, 0000

Norio IWASE

Faculty of Mathematics,

Kyushu University,

Fukuoka 819-0395, Japan

E-mail address: iwase@math.kyushu-u.ac.jp

TMNA : Volume 00 – 0000 – No 00

...

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